Number Theory

    

Proof of the Lonely Runner Conjecture

Authors: Babacar Gueye

Consider k runners on a circular track of unit length. At t=0, all the runners are at the same position and start to run; the runners speeds are distincts. A runner is said to be lonely at time t, if he is at a distance of at least 1/k from every other. The lonely runner conjecture states that each runner is lonely at some times. It is said we not lost generality to assume that the runners have integer speeds. It is knew that the conjecture is proved until seven runners at 2008. Then consider here integer speeds and prove the conjecture in general.

Comments: 8 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

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[v1] 2021-01-21 14:52:06

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